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3 years ago

Daija graphed the relationship modeled by the equation y = 4x.

Mathematics

1 answer:

GenaCL600 [577]3 years ago

3 0

The y intercept is (0,0) and the slope is 4

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Implicit diffrention problems I am really stuck on

AysviL [449]

Answer:

$\frac{dy}{dx} =\frac{4x^3+3x^2y-5y^2}{10xy-3y^2-x^3}$

Step-by-step explanation:

solving for dy/dx

multiply the equation out to remove parentheses

$x^4 + x^3y = 5xy^2 -y^3$

now differentiating in terms of x ( $\frac{dy}{dx}$ )

$4x^3 +3x^2y + x^3(\frac{dy}{dx} ) = 5y^2 + 10xy(\frac{dy}{dx} )-3y^2(\frac{dy}{dx} )$

isolating dy/dx to one side

$4x^3 +3x^2y - 5y^2= 10xy(\frac{dy}{dx} )-3y^2(\frac{dy}{dx} )-x^3(\frac{dy}{dx} )$

$4x^3 +3x^2y - 5y^2= \frac{dy}{dx}(10xy-3y^2-x^3)$

$\frac{dy}{dx} =\frac{4x^3+3x^2y-5y^2}{10xy-3y^2-x^3}$

5 0

3 years ago

Market researchers were interested in the relationship between the price of bobbleheads and the demand of

damaskus [11]

Answer:

for each increase in prices by $1, the predicted demand decreases by 0.227 units.

Step-by-step explanation:

4 0

2 years ago

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

$\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$

so the left side is

$2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n$

Also recall that

$\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}$

so that the right side is

$b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)$

Solve for $c$ .

$2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}$

Now, the numerator increases more slowly than the denominator, since

$\dfrac{d}{dn}(2n(n-1)) = 4n - 2$

$\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2$

and for $n\ge5$ ,

$2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2$

This means we only need to check if the claim is true for any $n\in\{1,2,3,4\}$ .

$n=1$ doesn't work, since that makes $c=0$ .

If $n=2$ , then

$c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0$

If $n=3$ , then

$c = \dfrac{12}{2^3 - 6 - 1} = 12$

If $n=4$ , then

$c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N$

There is only one value for which the claim is true, $c=12$ .

3 0

2 years ago

Im asking for you're help Citizen I have a question for you Me

Studentka2010 [4]

Answer:

No idea

Step-by-step explanation:

No idea for that either

8 0

2 years ago

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Mai conducted an experiment by flipping a fair coin 200 times. The coin landed heads up 110 times. Which statement about

Nitella [24]

Answer:

B

Explanation:

Theoretical probability is a method to express the likelihood that something will occur. It is calculated by dividing the number of favorable outcomes by the total possible outcomes.

The empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

8 0

3 years ago

Read 2 more answers